I can’t see the screenshots you gave above.
And the description given, does not help much to know what’s happening.
From my own using the plugin, only the person who creates the assignment can edit it.
And when you assign a user as teacher, the person is able to create lecture, assignment, under the ‘Courseware’->’Home’ page

Sorry i don’t think i can help to fix that.
I suggest you start with clean install, WordPress, BuddyPress, and Courseware plugin first, before adding the rest of the plugins. See if you can get it to work.